2020/03/31 by Manouchehr Zaker, Zaker, Manouchehr
Computer Science · Mathematics · #05C15 #05C20 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2003.14233
openalex publication_date 2020/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Grundy number of a graph G is the maximum number of colors used by the First-Fit coloring of G and is denoted by Γ(G). Similarly, the \rm b-chromatic number \rmb(G) of G expresses the worst case behavior of another well-known coloring procedure i.e. color-dominating coloring of G. We obtain some families of graphs F for which there exists a function f(x) such that Γ(G)≤ f(\rmb(G)), for each graph G from the family. Call any such family (Γ,b)-bounded family. We conjecture that the family of \rm b-monotone graphs is (Γ,b)-bounded and validate the conjecture for some families of graphs.